Li S.Z., Jain A.K. (eds.) Encyclopedia of Biometrics

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To provide a little more balance between conve-

nience and security, a multimodal system could still

be employed, but only with one or two randomly

selected biometric modalities required for authentica-

tion/identiﬁcation. Variations could also be introduced

within a single modality (e.g., requiring submission of

a right index ﬁnger, one day, and submission of a left

thumb on the nex t day).

The authentication/identiﬁcation systems could also

be designed to issue randomized as well as cued

challenges – even if the original submission would

otherwise have been acceptable. At the very least, this

implementation w ould provide the opportunity to ob-

tain two biometric samples. Where the samples are un-

usually similar , extra caution might be merited in case a

spoof is involv ed, as the likelihood that a person will be as

infallible as to place their biometric so consistently is slim.

Finally, biometric systems can be deployed and

designed so as to focus on internal or subcutaneous

characteristics that are generally much more difﬁcult

to capture surreptitiously, as well as to forge or modify.

Biometrics and Fraud: Looking

to the Future

While a lot of focus has been placed on the design and

utilization of biometrics to deter, inhibit, and –

to a lesser degree – mitigate non-biometric fraud,

comparatively little attention has been paid to the con-

sequences and implications when fraudsters are success-

ful in compromising biometric data. Because biometric

characteristics are so intrinsic and relatively immutable,

this is an issue of particular concern that can impact the

successful deployment of the technologies.

Cancelable/Changeable Biometrics

To address concern over the immutability of bio-

metrics, research has been conducted by entities like

IBM and the Korean Biometrics Engineering Research

Center into cancellable biometrics, also known as

changeable biometrics. The high-level concept of such

research has been to look into altering biometric data

that is captured before it is actually fully processed and

stored in template form. In this way, a compromised

biometric can theoretically be revoked and a new algo-

rithm can generate a novel distortion of the affected

individual’s biometric characteristic – essentially giving

them a new biometric.

However, one should keep in mind that if a fraud-

ster is able to get hold of the original source biometric

characteristic (or an equivalent spoof), this approach

would not sufﬁce, as the fraudster would then still be

able to regenerate a new cancelable/changeable bio-

metric characteristic just as easily as the legitimate

bearer of the original source biometric.

Nominal Identities Versus Biometric

Identities

As biometric systems increasingly protect sensitive

data and items or access privileges of high value, the

incentive fraudulent activity to exploit them will also

increase. And at some point, as the case has been with

virtually every major security technology in the past,

biometric data w ill be compromised.

One of the important ways in which the impact of

such compromise can be mitigated is to sever, when-

ever feasible and reasonable, the connection between

Examples of liveness detection methods for five established biometric modalities include:

Fingerprint Face Iris Hand geometry Voice recognition

Spectroscopic

analysis

Reactivity to Cues,

Commands, and stimuli

(e.g., – blinking)

Photonic and

spectrographic

analysis

Required contact with

specifically- placed

prongs

Recitation of

randomly generated

passphrases

Temporal

variation in

perspiration

Reactivity to stimuli

(e.g., – pupil

dilation)

Ink/Dye detection

Timestamping and

byte scrambling

590

Fraud Reduction, Overview

an indiv idual’s nominal identity and their biometric

identity. If, for instance, a deployment merely

requires a de termination as to whether a given indi-

vidual, represented by their biometric characteristics,

should be granted access to a given secure location,

then there is no need to link permanently the indiv i-

dual’s name and background information to their

biometric data after an initial background check has

been conducted.

Whereas names have often served as proxies for

trustworthiness or transactional histories, biometrics

can now serve this purpose going forward. With

biometrics there is also the possibility of selecting dif-

ferent biometric aspects for accreditation or validation

given each distinct application or deployment. A sing le

biometric characteristic, thus, has the ﬂexibility to serve

in a variety of functions that process that biometric

differently – without making that biometric into a

universal identiﬁer rife with the problems of overuse

that have plagued the US social security number.

In the scenario described above, if a fraudster com-

promises one biometric system, the damage is miti-

gated insofar as other systems and deployments may

still be protected, in addition to sensitive and private

information tied to one’s nomi nal identity.

Valuing Biometric Data

One of the remaining challenges with respect to

biometrics and fraud is the determination of how to

value biome tric data. This is especially important as

fraudsters increasingly target not just data protected by

biometrics, but biometric data, itself.

Traditionally, items have been valued based on

three factors:



Scarcity



Uniqueness



Demand

With biometrics, however, such a framework for asses-

sing value is of little use: virtually each and every given

biometric characteristic is inherently distinct (if not

unique), scarce, and of high demand for both the

possessor and potential imposters/fraudsters. It

would seem, therefore, that all biometric characteris-

tics should be deemed priceless or at least assigned

extremely lofty values.

However, this would be impractical in an age of risk

calculations and need by insurance companies, govern-

ments, and other entities realistically to quantify the

impact and cost of fraud. Therefore, valuation of a

biometric is best conducted according to a different

set of three factors:



Value of the Biometrically-Protected Item or Privilege



Range of Utility



Spoofabilit y

In addition, whenever a biometric system is designed,

careful consideration needs to be taken as to whether

templates or images should be used. Generally, images

will be more valuable from perspectives concerned

with forensics, interoperability, and scalability.

Templates, however, will be more desirable from an

identity-protecting perspective. Thus, from a fraud

reduction perspective, the guiding principle should

be that templates, which are more limited than images,

normally, should be employed whenever possible in

lieu of images. To achieve this balance, a negative

incentive should be implemented such that there will

be stiffer legal penalties for compromised biometric

image data versus biometric template data.

Related Entries

▶ Asset Protection

▶ Binding of Biometric and User Data

▶ Biometric Encryption

▶ Consumer Recognition

▶ Forgery Sign

▶ Fraud Reduction, Applications

▶ Liveness and Anti-Spooﬁng

▶ Spooﬁng

▶ Time and Attendance

References

1. Study Report on Biometrics and E-Authentication. INCITS/M1

Ad Hoc Group on Biometrics in E-Authentication (2006)

2. Anderson, K.: Consumer Fraud in the United States: Second

Survey. Federal Trade Commission, Washington, DC (2007)

3. Lee, V. et al.:Transcript of Authentication Technologies FTC

Proof Positive Workshop Session. Federal Trade Commission,

Washington, DC (2007)

Fraud Reduction, Overview

591

4. Fraud and Error in the Beneﬁt System: October 2006 to

September 2007. UK Department for Work and Pensions, Infor-

mation Directorate (May 2008)

5. Progress in Tackling Beneﬁt Fraud: Thirty-ﬁrst Report of Session

2007–2008. UK House of Commons, Committee of Public

Accounts (2 June 2008)

6. Counting the cost of UK fraud, BBC News, 24 November 2005.

http://news.bbc.co.uk/1/hi/business/4463132.stm (29 September

2008)

7. Woolcock, N.: Cost of fraud spirals to £40bn, TimesOnline,

9 September 2006. http://www.timesonline.co.uk/tol/news/uk/

article633540.ece (29 September 2008)

8. Ratha, N. et al.: Cancelable Biometrics: A Case Study in Finger-

prints (2006)

9. Unisys. Consumers Worldwide Overwhelmingly Support

Biometrics for Identity Veriﬁcation, 26 April 2006. Press release

(30 September 2008)

10. Use of Biometric Identiﬁcation Technology to Reduce Fraud

in the Food Stamp Program, United States Department of

Agriculture, Food and Nutrition Service, December 1999.

http://www.fns.usda.gov/oane/MENU/Published/fsp/FILES/

ProgramIntegrity/biomeval.htm (30 September 2008)

11. Identity Fraud: Prevalence and Links to Alien Illegal Activities,

United State General Accounting Ofﬁce, 25 June 2002. http://

www.gao.gov/new.items/d02830t.pdf (30 September 2008)

12. Martinez-Diaz, M. et al.: Hill-Climbing and Brute-Force

Attacks on Biometric S ystems: A Case Study in Match-on-Car d

Fingerprint Veriﬁcation, http://ﬁerrez.ii.uam.es/docs/2006_

ICCST_HillClimbingAttackMoC_Martinez.pdf (30 September

2008)

13. Schuckers, S. et al.: Issues for Liveness Detection in Biometrics.

http://www.biometrics. org/html/bc2002_sept_program/2_

bc0130_DerakhshabiBrief.pdf (30 September 2008)

Freeman Chain Code (FCC)

Freeman Chain Code (FCC) is a compact method

for representing the contours of an object, ﬁrst made

popular by Herbert Freeman.

▶ Hand Data Interchange Format, Standardization

Function Creep

This refers to the use of data beyond the purposes

originally intended at the time of data collection. For

biometrics, this usually means using the data for

purposs other than identiﬁcation, as when a face

image is used to determine gender or ethnicity.

▶ Privacy Issues

Fundamental Frequency,

Pitch, F0

The fundamental frequen cy or F0 is the frequency at

which vocal chords vibrate in voiced sounds. This

frequency can be identiﬁed in the sound produced,

which presents quasi -periodicity, the pitch period

being the fundamental period of the signal (the inverse

of the fundamental frequency). Pitch is more often

used to refer to how the fundamental frequency is

perceived.

▶ Speech Analysis

Fusion Network Topology

The network architecture including sensors, commu-

nication channels, and fusion processing. The fusion

processing may be distributed due to physical con-

straints in the system. If a communication channel

between two sensors is long, it may be beneﬁcial to

fuse all the sensors at one end of the channel so that

only the single fused decision is sent through the

channel. The topology is directly impacted by the

physical layout of the sensor network.

▶ Fusion, Decision Level

Fusion, Biometric

See Multi-biometrics.

▶ Biometric Algorithms

▶ Multibiometrics and Data Fusion Standardization

▶ Multiple Experts

592

Freeman Chain Code (FCC)

Fusion, Confidence Level

▶ Fusion, Score-Level

Fusion, Data Level

▶ Fusion, Sensor-Level

Fusion, Decision-Level

LISA OSADCIW,KALYAN VEERAMACHANENI

Syracuse University, Syracuse, NY, USA

Synonyms

Distributed detection; Distributed inference making;

Multiple classiﬁer fusion; Statistical signal processing

Definition

Decision level fusion falls under a broader area known

as distributed detection systems and is the process of

selecting one hypothesis from multiple M hypotheses

given the decisions of multiple N sensors in the presence

of noise and interference. In biometrics, decision level

fusion creates a single decision from typically two

hypotheses, imposter or genuine user, from multiple bio-

metric sensor decisions, which may or may not be identi-

cal sensors. Often, decision leve l fusion is implemented to

save communication bandwidth as well as improv e deci-

sion accuracy. A statistical performanc e model for each

biometric sensor is needed a priori to support the system

wide optimization in terms of two error rates: false accep-

tance rate, admitting an imposter, and false rejection rate,

rejecting the genuine user. A weighted sum of these two

errors is a useful objective function. This provides the

designer with the ﬂexibility to weigh one error more than

the other error. Decision lev el fusion may be done at one

proce ssor, centrally, or at multiple processors, distributed.

Introduction

In biometric decision level fusion, the biometric sensors

send their ﬁnal decisions through a communication

network that ﬁnally fuses these decisions at a fusion

center. Optimal decision fusion theory can be applied

to these problems. In distributed detection systems, the

number of decisions a sensor can make varies as well as

the

▶ fusion network topology. It may be more advan-

tageous to fuse a few sensors at a local node before

transmitting the information over a long distance to

the ﬁnal fusion processor [1]. This complicates the

fusion problem by introducing different fusion net-

work topologies. Decision level fusion remains at the

foundation of the problem, however.

The decision level fusion problem in the biometric

area is typically one in identifying the user as a genuine

user or an imposter with the ﬁnal decision made by a

central fusion processor [2–5]. This is referred to as a

▶ parallel fusion network. The advantages of fusion are

twofold. The ﬁrst advantage is a more accurate ﬁnal

decision by using multimodal, multiple and diverse,

biometric sensors, which provide signiﬁcantly more

information to base a decision. Secondly, communica-

tion bandwidth needs, which are great as more sens ors

are networked, remain relatively constant if the deci-

sions instead of the full observation or measurement

are communicated.

The fusion accuracy of the sensor decisions relies

on the accuracy of the statistical models for the sensors

and an optimally designed fusion rule. The biometric

veriﬁcation problem may be posed as a

▶ binary

hypothesis testing problem with the match score(s)

serving as observations. The two hypotheses are

: Imposter Identiﬁed and

: Genuine User Identiﬁed

Probability of false alarm,

¼ Pðu ¼ 1jH

Þð1Þ

and probability of false rejection,

¼ Pðu ¼ 0jH

Þð2Þ

In the Bayesian formulation, these two errors are

weighted by costs and summed into a single cost func-

tion called the Bayesian risk function. The Bayesian

risk function is

R ¼ PðH

ÞC

 P

þ PðH

ÞC

 P

; ð3Þ

Fusion, Decision-Level

593

where PðH

Þ, a priori probability of an imposters,

PðH

Þ a priori probability of a genuine user C

, cost

of false acceptance, and C

, cost of false rejection. In

the worst-case scenario, one assumes equal a priori

probabilities. Thus, we get

R ¼ C

 P

þ C

 P

: ð4Þ

We can rewrite Eq. 4, using a single cost factor by

replacing the cost of false acceptance by

¼ 2  C

: ð5Þ

This simpliﬁes the problem to one design parameter to

optimize if the a priori probabilities of genuine users

and imposters are assumed to be ﬁxed.

Decision Level Fusion with Single Bit

Information

Often Gaussian distribution functions are used as the

statistical sensor models for a binary hypothesis problem.

Each sensor has a different Gaussian distribution func-

tion as shown in Fig. 1 for each hypothesis: genuine user

and imposter. Higher observation values are t ypically

associated with a positive user identiﬁcation or the

genuine user hypothesis. This leads to the distribution

on the right side of the plot in Fig. 1. The imposter has a

lower mean. Sensor 1 must measure a score that exceeds

a threshold for comparison purpose to decide if it has the

genuine user . The error rates are simply the areas under

the distribution corresponding to the opposite hypothe-

sis or wrong side of the threshold. False acceptance

probability is the area to the right of the threshold

under the imposter distribution. False rejection proba-

bility is the area to the left of the threshold under the

genuine user distribution. A single bit of 1 denotes that

the user is detected while the 0 is for the imposter [7].

The threshold divides the entire decision region

into region of acceptance and region of rejection. If a

user’s matching score happens to fall above the thresh-

olds, he/she is considered as genuine. If the user’s

matching score falls below threshold he/she is consid-

ered as imposte r [1, 2, 5, 6]. This process using the

threshold, l

, for sensor i is given by

1; y

>¼ l

0; y

< l



8i ð6Þ

Let ½u¼ u

; u

; ...; u

½, be the combine d vector

of decisions represented by 1s and 0s for all the

sensors. T hese decisions are combined using a fusion

rule of

¼ f ð½uÞ: ð7Þ

The complete set of fusion rules for the 2-sensor case is

given in Table 1 [1]. There are 16 possible rules

for 2 sensors or (2

)

with N sensors as 2. The fusion

rule can be written as a 4-bit vector, where each

bit represents the ﬁnal fused decision given the

Fusion, Decision-Level. Figure 1 Illustration of thresholding process, Decision Regions, and Error Regions, for given

Gaussian conditional density functions.

594

Fusion, Decision-Level

sensor decisions, [u

]. Since, there are two hypo-

theses, the fusion rules are bas ed on Boolean logic.

For example, in Table 1, f

is a rule based on AND

logic. The ﬁnal decision is ‘‘1’’ only when both the

sensors say ‘‘1’’ and is ‘‘0’’ otherwise. Similarly, f

‘‘NAND’’, and f

is ‘‘OR’’.

For 3 sensors, there are 8 possible vectors requiring

a fused decision. Hence, the fusion rule is 8 bits long,

and the number of possible fusion rules for this prob-

lem is (2

)

or 64 rules for 3 sensors.

The error probabilities as in Eqs. 1 and 2 for the

entire system after fusion is estimated using

½u

Pðu

¼ 1j½u; H

ÞPð½ujH

Þ: ð8Þ

Assuming independence, Eq. 8 can be calculated using

the statistical models and

½u

Pðu

¼ 1j½u; H

i¼1

Pðu

½u

Pðu

¼ 1j½u; H

i¼1

Pðy

Þdy

ð9Þ

In case of correlation [8], however, the product dis-

appears resulting in a multivariate integral or

½u

Pðu

¼1j½u;H



;:Y

ðy

;...;y

Þdy

;...;dy

ð10Þ

Similarly,

½u

Pðu

¼0j½u;H

ÞPð½ujH

Þ: ð11Þ

Assuming independence, (11) can be calculated

using

½u

Pðu

¼0j½u;H

i¼1

Pðu

Þ: ð12Þ

In case of correlation, the multivariate integral arises as

before giving

½u

Pðu

¼0j½u;H



;...;Y

ðy

;...;y

Þdy

;...;dy

ð13Þ

This multivariate integral can only be calculated using

numerical methods. Since there are 2

combinations

of local decisions for N sensors, this integral must be

evaluated 2

1 times to estimate each error. This

operation can be ver y expensive computationally as

the number of sensors increases. An alternative is

using the Bahadur–Lazarfeld expansion, which enables

the estimation of the error probabilities using ‘‘n

1’’

evaluations of integrals [8].

The Bayesian risk function is now given by,

R ¼ P

Pðu

¼ 1j½u; H

ÞþP

Pðu

¼ 0j½u; H

Þ:

ð15Þ

Optimal Fusion Rule

For independent sens ors, however, the optimal fusion

rule is the

▶ likelihood ratio test [5]. For ﬁxed thresh-

olds, the optimal fusion rule can be obtained by using

the likelihood ratio as in

Pðu

; u

u

Pðu

; u

u

¼ 1

¼ 0

ðC

 C

ðC

 C

ð16Þ

Fusion, Decision-Level. Table 1 All Possible Fusion Rules for 2 Sensors

00 0000000011 1 1 1 1 1 1

01 0000111100 0 0 1 1 1 1

10 0011001100 1 1 0 0 1 1

11 0101010101 0 1 0 1 0 1

Fusion, Decision-Level

595

Pðu

; u

u

Þ in (16) can be replaced by

i¼1

Pðy

Þdy

in case of independence or



;...;Y

ðy

;...;y

Þdy

;...;dy

in case of correlation. Optimal fusion rule can be

employed when the thresholds are ﬁxed. The optimal

fusion rule as in Eq. 16 minimizes the Bayesian risk

function.

In the case of independence [5], the optimum rule

simpliﬁes to

i¼1

log

1  F



þð1  u

Þlog

1F



¼ 1

¼ 0

log

2C



ð17Þ

Independent Pair of Biometric Sensors

Consider two sensors with conditional distributions

under both the hypotheses given by the familiar

Gaussian distribution. A Gaussian distribution is char-

acterized by N ðm; sÞ with a different mean, m, and

standard deviation, s, for each hypothesis as men-

tioned earlier. Table 2 gives the parameters of the

Gaussian distributions used for the 2 sensors in this

example. In Table 3, the threshold that achieves the

false alarm rate and false rejection rate given is speci-

ﬁed for both sensors. Using these thresholds as well

as the error rates in the optimal fusion rule of Eq. 17,

we give the rules in the right column for the speciﬁed

costs in the left. Thus, different rules become optimum

as the error rates are weighted differently. If the sensor

is replaced with a more accurate biometric sensor, the

rule selection will change. Finally, if the sensors are

correlated, the original rule in Eq. 16 must be applied

and performance computed accordingly.

Related Entries

▶ Multiple Experts

References

1. Varshney, P.K.: Distributed Detection and Data Fusion, Springer.

Springer-Verlag, New York, Inc (1997)

Fusion, Decision-Level. Table 4 Optimal Fusion Rule

Under Assumption of Independence

CFA Optimal Fusion Rule

0.2 Majority Voting Rule

0.6 Majority Voting Rule

1 (1 OR 2) AND 3

1.2 (1 OR 2) AND 3

1.5 (1 OR 2) AND 3

1.9 (1 OR 2) AND 3

Fusion, Decision-Level. Table 3 Thresholds for the 3 Sensors for Single Bit Information

Sensor Threshold FAR FRR

1 95.945029260756 0.13409060569213 0.00007790554000

2 185.799498919171 0.01245661704014 0.00223574300430

Fusion, Decision Level. Table 2 Means and Standard Deviations of the Gaussian Distributions Under both the

Hypothesis for Different Sensors

Hypothesis/Paremeter H

Sensor 1 47.375 43.864 144.514 12.843

Sensor 2 67.755 52.633 251.209 23.008

596

Fusion, Decision-Level

2. Prabhakar, S., Jain, A.: ‘‘Decision-level Fusion in Fingerprint

Veriﬁcation’’, Pattern Recognit. 35, 861–874 (2002)

3. Osadciw, L., Varshney, P., Veeramachaneni, K.: ‘‘Optimum

Fusion Rules for Multimodal Biometric Systems’’, Foresti, G.L.,

Regazzoni, C.S., Varshney, P.K. Chap. 15, Multisensor Surveil-

lance Systems: The Fusion Perspective, Kluwer (2003)

4. Veeramachaneni, K.: ‘‘An Evolutionary Algorithm Based

Dynamic Thresholding for Multimodal Biometrics’’ Masters

thesis, School of Electrical and Computer Engineering, Syracuse

University (2003)

5. Chair, Z., Varshney, P.K.: ‘‘Optimal Data Fusion in Multiple

Sensor Detection Systems’’, IEEE Trans. Aerosp. Electron. Syst.

22(1), 98–101 (1986)

6. Tang, Z.-B., Pattipati, K.R., Kleinman, D.L.: ‘‘An Algorithm for

Determining the Decision Thresholds in a Distributed Detection

Problem’’. IEEE Trans. Syst. Man Cybern. 21, 231–237 (1991)

7. Veeramachaneni, K., Osadciw, L., Varshney, P.: «Adaptive Multi-

modal Biometric Management Algorithm «, IEEE Trans. Syst.

Man Cybern. 35 (2005)

8. Kam, M., Zhu, Q., Gray, W.S.: ‘‘Optimal Data Fusion of Corre-

lated Local Decisions in Multiple Sensor Detection Systems,’’

IEEE Trans. Aerosp. Electron. Syst. 28, 916–920 (1992)

Fusion, Feature-Level

ARU N ROSS

West Virginia University, Morgantown, WV, USA

Synonym

Feature Fusion

Definition

In feature-level fusion, the feature sets originating from

multiple biometric sources are consolidated into a

single feature set by the application of appropriate

feature normalization, transformation, and reduction

schemes. The primary beneﬁt of feature-level fusion is

the detection of correlated feature values generated by

different biometric algorithms thereby identifying a

compact set of salient features that can improve recog-

nition accuracy. Eliciting this feature set typically

requires the use of

▶ dimensionality reduction meth-

ods and, therefore, feature-level fusion assumes

the availability of a large number of training data.

Feature-level fusion algorithms can also be used for

template update or template improvement.

Introduction

Feature level fusion is an example of an early fusion

strategy, i.e., the biometric evidence from multiple

sources are consolidated before invoking the matcher.

In this scheme, multiple feature sets are integrated in

order to gen erate a single template that is expected to

be more robust than the individual feature sets. When

the feature sets to be integrated are homogeneous (e.g.,

multiple measurements of a person’s hand geometry),

a single feature vector can be computed as a weighted

average of the individual feature sets. When the feature

sets are nonhomogeneous (e.g., features of different

biometric modalities like face and hand geometry),

they can be concatenated to form a single feature set.

Feature selection schemes are employed to reduce

the dimensionality of the ensuing feature set [1]. Con-

catenation is not possible when the feature sets are

incompatible (e.g., ﬁngerprint minutiae and eigen-

face coefﬁcients).

If the feature sets to be combined originate from

the same feature extraction algorithm (thus, a single

modality is assumed) then feature level fusion can be

used for template update or template improvement as

discussed in the following section.

1. Template update: The template in the database

can be updated based on the evidence presented

by the current feature set in order to reﬂect (possi-

bly) permanent changes in a person’s biometric.

Hand geometry systems use this process to update

the geometric measurements stored in the database

in order to account for changes in an individual’s

hand over a period of time. A simple scheme would

be to take the average of the two feature vectors

corresponding to the two instances of the biometric

signal and use the average feature vector as the

new templa te (Fig. 1).

2. Template improvement: In the case of ﬁngerprints,

the minutiae information available in two impres-

sions can be combined by appropriately aligning

the two prints and removing duplicate minutia

thereby generating a larger minutia set. This process,

known as template improvement, can also be used to

remove spurious minutiae points that may be pres-

ent in a feature set. While template update is used to

accommodate temporal changes in a person’s bio-

metric, the purpose of template improvement is to

increase the number of features (and decrease the

number of spurious features) in the template.

Fusion, Feature-Level

597

Several template improvement algorithms have been

discussed in the literature for ﬁngerprints. Jiang and

Ser [2] propose a template improvement scheme where

a reliability measure is associated with each extracted

minutia point. This reliability measure is updated as

minutiae evidence from newly acquired impressions is

made available. The parameters of a minutia point

(i.e., its x-y location and orientation) are updated

via a weighted average scheme; even the ‘‘type’’ of

the minutiae (i.e., ridge-ending or ridge-bifurcation)

is altered if necessary. Template improvement is appli-

cable only when the new ﬁngerprint impression is

accurately aligned with the stored one. The authors

use the match score to determine if two impressions

are accurately aligned. During the veriﬁcation stage,

only those minutia points whose reliability measure is

above a certain threshold are used in the matc hing

process. The authors show that their scheme results

in (1) the elimination of spurious minutiae points,

(2) the addition of missed minutiae points, (3) the

relabeling of incorrect minutiae types and, conse-

quently, (4) a general improvement in matching per-

formance. Other algorithms for minu tiae template

improvement have been discussed in [3, 4].

Feature Fusion Scheme

How does one consolidate feature sets originating from

different algorithms and modalities? Feature level

fusion is difﬁcult to achieve in such cases because of

the following reasons:

1. The relationship between the feature spaces of dif-

ferent biometric systems may not be known.

2. The feature sets of multiple modalities may

be incompatible. For exam ple, th e min utiae set

of ﬁngerprints and the eigen-coefﬁcients of

face are irreconcilable. One is a variable length

feature set (i.e., it varies across images) whose

individual values parameterize a m inutia point;

the other is a ﬁxed length feature set (i.e., all

images are represented by a ﬁxed number of

eigen-coefﬁcients) whose individual values are

scalar entities.

3. If the two feature sets are ﬁxed length featu re vec-

tors, then one could consider augmenting them to

generate a new feature set. However, concatenating

two feature vectors might lead to the

▶ curse-of-

dimensionality problem [5] where increasing the

number of features might actually degrade the sys-

tem performance especially in the presence of small

number of training samples. Although the curse-

of-dimensionality is a well known problem in pat-

tern recognition, it is particularly pronounced in

biometric applications because of the time, effort

and cost required to collect large amounts of bio-

metric (training) data.

4. Most commercial biometric systems do n ot pro-

vide access to the feature sets us ed in their pro-

ducts. Hence, very few biome tric researchers have

Fusion, Feature-Level. Figure 1 A template update procedure may be viewed as a feature fusion scheme. In this

example, the nine-dimensional feature set of a user (‘‘Feature Set 1’’) is updated based on the evidence

presented by the current feature set (‘‘Feature Set 2’’), via the averaging scheme.

598

Fusion, Feature-Level

focused on integration at the feature level and

most of them generally prefer fusion schemes

that use match scores or decision labels.

If the length of each of the two feature vectors to

be consolidated is ﬁxed across all users, then a feature

concatenation scheme followed by a dimension-

ality reduction procedure may be adopted. Let X ¼

,...,x

} and Y ¼ {y

,...,y

} denote two

feature vectors (X 2 R

and Y 2 R

) representing the

information extracted from two different biometric

sources. The objective is to fuse these two feature sets

in order to yield a new feature vector, Z, that would

better represent an individual. The vector Z of di-

mensionality k, k < (m þ n), can be generated by

ﬁrst augmenting vectors X and Y, and then performing

feature selection or feature transformation on the re-

sultant feature vector in order to reduce its dimension-

ality. The key stages of such an approach are described

as follows (also see Fig. 2).

Feature Normalization

The individual feature values of vectors X ¼ {x

,...,

} and Y ¼ {y

,...,y

} may exhibit signiﬁcant

differences in their range as well as form (i.e., distribu-

tion). Augmenting such diverse feature values will

not be appropriate in many cases. For example, if the

’s are in the range [0,100] while the y

’s are in

the range [0,1], then the distance between two aug-

mented feature vectors will be more sensitive to the x

’s

than the y

’s. The goal of feature normalization is to

modify the location (mean) and scale (variance) of

the features values via a transformation function in

order to map them into a common domain. Adopting

an appropriate normalization scheme also helps

address the problem of outlier s in feature values.

While a variety of nor malization schemes can be

used, two simple schemes are discussed here: the

min–max and median normalization schemes.

Let x and x

denote a feature value before and after

normalization, respectively. The min–max technique

computes x

x  minðF

maxðF

ÞminðF

; ð1Þ

where F

is the function which generates x, and

min(F

) and max(F

) represent the minimum and

maximum of all possible x values that will be observed,

respectively. The min–max technique is effective when

the minimum and the maximum values of the compo-

nent feature values are known beforehand. In cases

where such information is not available, an estimate

of these parameters has to be obtained from the avail-

able set of training data. The estimate may be affected

by the presence of outliers in the training data and this

makes min–max normalization sensitive to outliers.

The median normali zation schem e, on the other

hand, is relatively robust to the presence of noise in

the training data. In this case, x

is computed as

x  medianðF

medianðjðx  medianðF

ÞÞjÞ

: ð 2Þ

The denominator is known as the Median Absolute

Deviation (MAD) and is an estimate of the scale

parameter of the feature value. Although, this nor-

malization scheme is relatively insensitive to outliers,

it has a low ef ﬁciency compared to the mean and

standard deviation estimators. Normalizing the fea-

ture values via any of these techniques results in

modiﬁed feature vectors X

¼fx

; x

; ...x

g and

¼fy

; y

; ...y

g: Feature normalization may not

be necessary in cases where the feature values pertain-

ing to multiple sources are already comparable.

Fusion, Feature-Level. Figure 2 The procedure adopted

by Ross and Govindarajan [1] to perform feature level

fusion.

Fusion, Feature-Level

599